I've found Patterson's history to be fairly accurate, but as with all sources like this it's best to try to find a corroborating source as well.
I note that the Chalmers of Gadgirth are mentioned in Balfour Paul's Scots Peerage. You may want to use that as well when you're working through the lineage.
There is an easy link to all the volumes here on Wikipedia, and this is a link directly to the index page for the Chalmers of Gadgirth. (Be patient for it to load, as I've added a search link so that Gadgirth will be apparent on these dense pages.)
Since the family is concentrated in Ayrshire, you might find additional ideas for sources on our Ayrshire page, though if you're using Patterson, you're probably aware of most of them already.
Hope this is helpful.